.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/generated/scripts_synth_data/three_survey_lines_smt_emcee.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_generated_scripts_synth_data_three_survey_lines_smt_emcee.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_generated_scripts_synth_data_three_survey_lines_smt_emcee.py:


Invert three surveys line for a thin plate using the surrogate model
====================================================================

.. raw:: html

   <!-- Please leave the cell below as it is -->

.. GENERATED FROM PYTHON SOURCE LINES 13-18

|Open In Colab|

.. |Open In Colab| image:: https://img.shields.io/badge/open%20in-Colab-b5e2fa?logo=googlecolab&style=flat-square&color=ffd670
   :target: https://colab.research.google.com/github/inlab-geo/cofi-examples/blob/main/examples/airborne_em/airborne_em_three_lines_transmitters.ipynb


.. GENERATED FROM PYTHON SOURCE LINES 21-40

.. raw:: html

   <!-- Again, please don't touch the markdown cell above. We'll generate badge 
        automatically from the above cell. -->

.. raw:: html

   <!-- This cell describes things related to environment setup, so please add more text 
        if something special (not listed below) is needed to run this notebook -->

..

   If you are running this notebook locally, make sure you’ve followed
   `steps
   here <https://github.com/inlab-geo/cofi-examples#run-the-examples-with-cofi-locally>`__
   to set up the environment. (This
   `environment.yml <https://github.com/inlab-geo/cofi-examples/blob/main/envs/environment.yml>`__
   file specifies a list of packages required to run the notebooks)


.. GENERATED FROM PYTHON SOURCE LINES 43-49

This notebook assumes that you have created a surrogate model by
executing the following two notebooks: - `Latin Hypercube
Sampling <./three_survey_lines_latin_hypercube_sampling.ipynb>`__ -
`Surrogate model
creation <./three_survey_lines_surrogate_model_creation.ipynb>`__


.. GENERATED FROM PYTHON SOURCE LINES 49-61

.. code-block:: Python


    # -------------------------------------------------------- #
    #                                                          #
    #     Uncomment below to set up environment on "colab"     #
    #                                                          #
    # -------------------------------------------------------- #

    # !pip install -U cofi
    # !pip install git+https://github.com/JuergHauser/PyP223.git
    # !git clone https://github.com/inlab-geo/cofi-examples.git
    # %cd cofi-examples/examples/vtem_max








.. GENERATED FROM PYTHON SOURCE LINES 63-69

.. code-block:: Python


    # If this notebook is run locally PyP223 and smt need to be installed separately by uncommenting the following lines, 
    # that is by removing the # and the white space between it and the exclamation mark.
    # !pip install git+https://github.com/JuergHauser/PyP223.git
    # !pip install smt








.. GENERATED FROM PYTHON SOURCE LINES 71-91

.. code-block:: Python


    import pickle
    import numpy
    import matplotlib.pyplot as plt
    from matplotlib.lines import Line2D
    import cofi
    import arviz
    from vtem_max_forward_lib import (
        problem_setup, 
        system_spec, 
        survey_setup, 
        ForwardWrapper, 
        plot_predicted_profile, 
        plot_transient, 
        plot_plate_faces, 
        plot_plate_faces_single
    )

    numpy.random.seed(42)








.. GENERATED FROM PYTHON SOURCE LINES 96-110

Background
----------

This example inverts three survey line of VTEM max data using the
vertical component for a thin plate target. It thus becomes possible to
invert for the easting,northing, depth of the plate reference point, the
plate dip and plate azimuth. Solving the forward problem, that is
calculating the objective function, usess the surrogate model that has
been created by the `Kriging
approach <./three_survey_lines_surrogate_model_creation.ipynb>`__
applied to the `latin hypercube
samples <three_survey_lines_latin_hypercube_sampling.ipynb>`__ of the
objective function.


.. GENERATED FROM PYTHON SOURCE LINES 113-116

Problem definition
------------------


.. GENERATED FROM PYTHON SOURCE LINES 116-130

.. code-block:: Python


    tx_min = 115
    tx_max = 281
    tx_interval = 15
    ty_min = 25
    ty_max = 176
    ty_interval = 75
    tx_points = numpy.arange(tx_min, tx_max, tx_interval)
    ty_points = numpy.arange(ty_min, ty_max, ty_interval)
    n_transmitters = len(tx_points) * len(ty_points)
    tx, ty = numpy.meshgrid(tx_points, ty_points)
    tx = tx.flatten()
    ty = ty.flatten()








.. GENERATED FROM PYTHON SOURCE LINES 132-139

.. code-block:: Python


    fiducial_id = numpy.arange(len(tx))
    line_id = numpy.zeros(len(tx), dtype=int)
    line_id[ty==ty_points[0]] = 0
    line_id[ty==ty_points[1]] = 1
    line_id[ty==ty_points[2]] = 2








.. GENERATED FROM PYTHON SOURCE LINES 141-158

.. code-block:: Python


    survey_setup = {
        "tx": tx,                                                   # transmitter easting/x-position
        "ty": ty,                                                   # transmitter northing/y-position
        "tz": numpy.array([50]*n_transmitters),                     # transmitter height/z-position
        "tazi": numpy.deg2rad(numpy.array([90]*n_transmitters)),    # transmitter azimuth
        "tincl": numpy.deg2rad(numpy.array([6]*n_transmitters)),    # transmitter inclination
        "rx": tx,                                                   # receiver easting/x-position
        "ry": numpy.array([100]*n_transmitters),                    # receiver northing/y-position
        "rz": numpy.array([50]*n_transmitters),                     # receiver height/z-position
        "trdx": numpy.array([0]*n_transmitters),                    # transmitter receiver separation inline
        "trdy": numpy.array([0]*n_transmitters),                    # transmitter receiver separation crossline
        "trdz": numpy.array([0]*n_transmitters),                    # transmitter receiver separation vertical
        "fiducial_id": fiducial_id,                                 # unique id for each transmitter
        "line_id": line_id                  # id for each line
    }








.. GENERATED FROM PYTHON SOURCE LINES 160-176

.. code-block:: Python


    true_model = {
        "res": numpy.array([300, 1000]), 
        "thk": numpy.array([20]), 
        "peast": numpy.array([175]), 
        "pnorth": numpy.array([100]), 
        "ptop": numpy.array([30]), 
        "pres": numpy.array([0.1]), 
        "plngth1": numpy.array([100]), 
        "plngth2": numpy.array([100]), 
        "pwdth1": numpy.array([0.1]), 
        "pwdth2": numpy.array([90]), 
        "pdzm": numpy.array([75]),
        "pdip": numpy.array([60])
    }








.. GENERATED FROM PYTHON SOURCE LINES 178-182

.. code-block:: Python


    forward = ForwardWrapper(true_model, problem_setup, system_spec, survey_setup,
                             ["pdip","pdzm", "peast", "ptop", "pwdth2"], data_returned=["vertical"])





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    ['pdip', 'pdzm', 'peast', 'ptop', 'pwdth2']




.. GENERATED FROM PYTHON SOURCE LINES 184-188

.. code-block:: Python


    # check the order of parameters in a model vector
    forward.params_to_invert





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    ['pdip', 'pdzm', 'peast', 'ptop', 'pwdth2']



.. GENERATED FROM PYTHON SOURCE LINES 190-193

.. code-block:: Python


    true_param_value = numpy.array([60.,65., 175., 30., 90.])








.. GENERATED FROM PYTHON SOURCE LINES 198-201

Ensemble method using the surrogate model
-----------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 201-207

.. code-block:: Python


    sm = None
    filename = "kriging_surrogate_model.pkl"
    with open(filename, "rb") as f:
       sm = pickle.load(f)








.. GENERATED FROM PYTHON SOURCE LINES 212-214

**Initialise a model for inversion**


.. GENERATED FROM PYTHON SOURCE LINES 214-219

.. code-block:: Python


    init_param_value = numpy.array([45, 90, 160, 35, 80])
    m_min = numpy.array([15, 35, 155, 30, 65])
    m_max = numpy.array([75, 145, 185, 40, 115])








.. GENERATED FROM PYTHON SOURCE LINES 224-226

**Define helper functions for CoFI**


.. GENERATED FROM PYTHON SOURCE LINES 226-242

.. code-block:: Python


    def my_objective(model):
        val=sm.predict_values(numpy.array([model]))[0][0]
        if val<1e-3:
            return 1e-3
        else:
            return val
        
    def my_log_likelihood(model):
        return -0.5 * my_objective(model)

    def my_log_prior(model):    # uniform distribution
        for i in range(len(model)):
            if model[i] < m_min[i] or model[i] > m_max[i]: return -numpy.inf
        return 0.0 # model lies within bounds -> return log(1)








.. GENERATED FROM PYTHON SOURCE LINES 247-249

**Define CoFI problem**


.. GENERATED FROM PYTHON SOURCE LINES 249-255

.. code-block:: Python


    my_problem = cofi.BaseProblem()
    my_problem.set_log_prior(my_log_prior)
    my_problem.set_log_likelihood(my_log_likelihood)
    my_problem.set_model_shape(len(init_param_value))








.. GENERATED FROM PYTHON SOURCE LINES 260-262

**Define CoFI options**


.. GENERATED FROM PYTHON SOURCE LINES 262-270

.. code-block:: Python


    nwalkers = 12
    ndim = len(init_param_value)
    nsteps = 5000
    walkers_start = init_param_value + 0.5 * numpy.random.randn(nwalkers, ndim)










.. GENERATED FROM PYTHON SOURCE LINES 272-276

.. code-block:: Python


    numpy.array([walkers_start[0]])






.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[ 45.24835708,  89.93086785, 160.32384427,  35.76151493,
             79.88292331]])



.. GENERATED FROM PYTHON SOURCE LINES 278-291

.. code-block:: Python


    inv_options = cofi.InversionOptions()
    inv_options.set_tool("emcee")
    inv_options.set_params(nwalkers=nwalkers, nsteps=nsteps, initial_state=walkers_start, progress=True)

    ######## Run it
    inv = cofi.Inversion(my_problem, inv_options)
    inv_result = inv.run()

    ######## Check result
    print(f"The inversion result from `emcee`:")
    inv_result.summary()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


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    The inversion result from `emcee`:
    ============================
    Summary for inversion result
    ============================
    SUCCESS
    ----------------------------
    sampler: <emcee.ensemble.EnsembleSampler object>
    blob_names: ['log_likelihood', 'log_prior']




.. GENERATED FROM PYTHON SOURCE LINES 296-299

Plotting
--------


.. GENERATED FROM PYTHON SOURCE LINES 299-329

.. code-block:: Python


    arviz.style.use("arviz-variat")

    var_names = [
        "Dip (°)",
        "Dip azimuth (°)",
        "Easting (m)",
        "Depth (m)",
        "Width (m)",
    ]

    true_values = [60, 65, 175, 30, 90]
    sampler = inv_result.sampler
    az_idata = inv_result.to_arviz(var_names=var_names)
    pc = arviz.plot_trace_dist(
        az_idata.sel(draw=slice(2000, None)),
        visuals={"xlabel_trace": False, "trace": {"color": "C0", "lw": 0.5}, "dist": {"color": "C0", "lw": 0.5}},
        figure_kwargs={"figsize": (12, 20), "constrained_layout": True},
    )
    var_list = list(az_idata.posterior.data_vars)
    for i, vname in enumerate(var_list):
        ax_kde = pc.iget_target(i, 0)
        ax_trace = pc.iget_target(i, 1)
        ax_kde.set_title(vname)
        ax_trace.set_title(vname)
        ax_kde.axvline(true_values[i], color="green", linestyle="--", lw=1, alpha=0.5)
        ax_trace.axhline(true_values[i], color="green", linestyle="--", lw=1, alpha=0.5)
        ax_trace.margins(x=0)





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_001.png
   :alt: Dip (°), Dip (°), Dip azimuth (°), Dip azimuth (°), Easting (m), Easting (m), Depth (m), Depth (m), Width (m), Width (m)
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 331-397

.. code-block:: Python


    from scipy.stats import gaussian_kde
    import arviz_base

    true_values_dict = {
        f"{var_names[i]}": true_param_value[i] for i in range(init_param_value.size)
    }

    # Set to True for KDE contours (old style), False for scatter (arviz 1.0 default)
    USE_KDE_CONTOURS = True

    arviz_base.rcParams["plot.max_subplots"] = 80

    if USE_KDE_CONTOURS:
        pm = arviz.plot_pair(
            az_idata.sel(draw=slice(4000, None)),
            marginal=True,
            triangle="lower",
            visuals={"scatter": False},
        )
        # Add KDE contours to off-diagonal panels
        posterior = az_idata.posterior.sel(draw=slice(4000, None))
        var_list = list(posterior.data_vars)
        n = len(var_list)
        for i in range(n):
            for j in range(n):
                if i <= j:
                    continue
                try:
                    ax = pm.iget_target(i, j)
                except (ValueError, IndexError):
                    continue
                x = posterior[var_list[j]].values.flatten()
                y = posterior[var_list[i]].values.flatten()
                kde = gaussian_kde(numpy.vstack([x, y]))
                xmin, xmax = x.min(), x.max()
                ymin, ymax = y.min(), y.max()
                xx, yy = numpy.mgrid[xmin:xmax:100j, ymin:ymax:100j]
                zz = kde(numpy.vstack([xx.ravel(), yy.ravel()])).reshape(xx.shape)
                ax.contourf(xx, yy, zz, levels=10, cmap="Blues")
                ax.contour(xx, yy, zz, levels=10, colors="grey", linewidths=0.5, alpha=0.5)
    else:
        pm = arviz.plot_pair(
            az_idata.sel(draw=slice(4000, None)),
            marginal=True,
            triangle="lower",
        )

    # Add reference values
    ref_vals = list(true_values_dict.values())
    n = len(ref_vals)
    for i in range(n):
        for j in range(n):
            try:
                ax = pm.iget_target(i, j)
            except (ValueError, IndexError):
                continue
            if i == j:
                ax.axvline(ref_vals[i], color="green", linestyle="--", lw=1, alpha=0.5)
            elif i > j:
                ax.plot(
                    ref_vals[j], ref_vals[i], "o",
                    color="yellow", markeredgecolor="k", ms=10, zorder=5,
                )





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_002.png
   :alt: three survey lines smt emcee
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 399-452

.. code-block:: Python


    arviz.style.use("arviz-variat")

    _, axes = plt.subplots(2, 2)
    axes[1,1].axis("off")
    plot_plate_faces(
        "plate_true", forward, true_param_value, 
        axes[0,0], axes[0,1], axes[1,0], color="purple", label="True model"
    )
    plot_plate_faces(
        "plate_init", forward, init_param_value, 
        axes[0,0], axes[0,1], axes[1,0], color="green", label="Starting model"
    )

    plt.tight_layout()

    posterior = az_idata.posterior
    var_list = list(posterior.data_vars)
    n_chains = int(posterior.sizes["chain"])
    n_draws = int(posterior.sizes["draw"])

    ichain = 0
    idraw = min(2500, n_draws - 1)
    sample = numpy.zeros(5)

    for idx, vn in enumerate(var_list):
        sample[idx] = float(posterior[vn].isel(chain=ichain, draw=idraw))

    plot_plate_faces(
        "plate_inverted", forward, sample, 
        axes[0,0], axes[0,1], axes[1,0], color="red", label="Posterior sample", linestyle="dotted"
    )

    point = Line2D([0], [0], label='Fiducial', marker='o', markersize=5, 
             markeredgecolor='orange', markerfacecolor='orange', linestyle='')

    handles, labels = axes[1,0].get_legend_handles_labels()
    handles.extend([point])

    axes[1,0].legend(handles=handles,bbox_to_anchor=(1.04, 0), loc="lower left")

    # plot 10 randomly selected samples of the posterior distribution
    for i in range(10):
        ichain = numpy.random.randint(0, n_chains)
        idraw = numpy.random.randint(min(2000, n_draws), n_draws)
        for idx, vn in enumerate(var_list):
            sample[idx] = float(posterior[vn].isel(chain=ichain, draw=idraw))
        plot_plate_faces(
            "plate_inverted", forward, sample, 
            axes[0,0], axes[0,1], axes[1,0], color="red", label="Posterior sample", linestyle="dotted"
        )





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_003.png
   :alt: three survey lines smt emcee
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_emcee_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 457-470

--------------

Watermark
---------

.. raw:: html

   <!-- Feel free to add more modules in the watermark_list below, if more packages are used -->

.. raw:: html

   <!-- Otherwise please leave the below code cell unchanged -->


.. GENERATED FROM PYTHON SOURCE LINES 470-476

.. code-block:: Python


    watermark_list = ["cofi", "numpy", "scipy", "matplotlib"]
    for pkg in watermark_list:
        pkg_var = __import__(pkg)
        print(pkg, getattr(pkg_var, "__version__"))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    cofi 0.2.11+71.gb28b5b0
    numpy 2.2.6
    scipy 1.17.1
    matplotlib 3.10.9




.. GENERATED FROM PYTHON SOURCE LINES 482-482

sphinx_gallery_thumbnail_number = -1


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 26.419 seconds)


.. _sphx_glr_download_examples_generated_scripts_synth_data_three_survey_lines_smt_emcee.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: three_survey_lines_smt_emcee.ipynb <three_survey_lines_smt_emcee.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: three_survey_lines_smt_emcee.py <three_survey_lines_smt_emcee.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: three_survey_lines_smt_emcee.zip <three_survey_lines_smt_emcee.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_